Video Transcript
Which of the following statements
must be true about a parallelogram? Option (A) it has four sides of
equal length. Option (B) it has four congruent
sides. Option (C) it has four right
angles. Option (D) it has one pair of
parallel sides. Or option (E) it has two pairs of
parallel opposite sides.
Here, we are considering different
statements that may or may not be true about a parallelogram. So let’s recall that a
parallelogram is defined as a quadrilateral with both pairs of opposite sides
parallel. This is what is given in the final
answer option (E). If having two pairs of opposite
sides parallel is what defines a parallelogram, then it must be true of every
parallelogram. But let’s consider what might be
happening in the other options. And to do this, let’s draw some
different parallelograms.
Here, we have a very typical
drawing of a parallelogram. It has got both pairs of opposite
sides parallel, so it is indeed a parallelogram. And here, we have a different
parallelogram with both pairs of opposite sides parallel. Now, it just so happens that this
parallelogram also has four congruent sides. In fact, we could call this special
type of parallelogram a rhombus, since this is defined as a parallelogram with four
congruent sides or indeed with four sides of equal length.
The two statements in option (A)
and (B) are equivalent and show the exact property that we have here. So why aren’t either of these the
answer to the question? Well, it’s because although they do
fit with a rhombus, which is a type of parallelogram, we can’t say that every
parallelogram has four congruent sides or four sides of equal measure. And remember, we are looking for a
statement which must be true about a parallelogram and indeed every
parallelogram. So we can eliminate answer options
(A) and (B).
Now, let’s consider option (C). As you might have guessed, we can
draw a parallelogram that also has four right angles. And of course, this is a rectangle,
which is defined as a parallelogram with four congruent angles. In the same reasoning as before, we
can note that although this parallelogram, which is a rectangle, does have four
right angles, not every parallelogram does. And since we are looking for a
statement that is true about every parallelogram, then option (C) is incorrect.
Now, let’s consider option (D),
which is the property that a parallelogram has one pair of parallel sides. It might be reasonable to say that
if a quadrilateral has two pairs of parallel sides, then it has one pair of parallel
sides. And if the answer option (E) wasn’t
available, then it might be a good choice. However, it does sound a little
more like the definition of a trapezoid, sometimes called a trapezium, depending on
where you live. A trapezoid is defined as a
quadrilateral with one pair, or exactly one pair, of parallel sides. Because of the fact that this
statement may be confused with the property of having just one pair of parallel
sides and the fact that we have this much better and more useful statement below
that a parallelogram must have two pairs of parallel sides, then we can eliminate
option (D).
Therefore, the statement that must
be true about a parallelogram is that given in option (E). It has two pairs of parallel
opposite sides.
